The new mean and standard deviation is 26 and 15, when each score in data set is multiplied by 5 and then 7 is added.
According to the question,
Original mean is 10 and original standard deviation is 5 . In order to find to new mean and standard deviation when each score in data set is multiplied by 5 and then 7 is added.
First "change of scale" when every score in a data set is multiplied by a constant, its mean and standard deviation is multiplied by a same constant.
Mean: 10*3 = 30
Standard deviation: 5*3 = 15
Secondly "change of origin" when every score in a data set by a constant, its mean get added or subtracted by the same constant and standard deviation remains constant.
Applying change of origin in the above mean and standard deviation
Mean: 30 - 4 = 26
Standard deviation: Remains same = 15
Hence, the new mean and standard deviation is 26 and 15, when each score in data set is multiplied by 5 and then 7 is added.
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The law of cosines states that, if 
is the angle between sides b and c,
So, plugging our values, we have
This is equal to
The rule for a 270° counterclockwise rotation is (x, y) ---> (y, -x).
So if you rotated (-5,5) 270° counterclockwise around the origin the new coordinates would be (-5,-5).
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The answer is 566m because 147 plus 147 and 136 plus 136 equals 566
